A de Bruijn graph of order \(m\) , is a directed graph with the vertex set \(\Sigma ^k\)  and \(uv\)  forms an arc iff \(u_2u_3\cdots u_k=v_1v_2\cdots v_{k-1}\) . There are many interesting results like For a de Bruijn graph of order \(k\)  whose \(|\Sigma |=2\)  with \(2^k\)  vertices, there exists \(2^{2^{k-1}-k}\)  different Hamiltonian cycles [1]}. Finding Hamiltonian cycle in a graph is a difficult computational problem, where de Bruijn graph made it easier and it is widely applied in genome assembly [2]}.
